Question

8.3 simplify rational exponents (homework) score: 10.05/25 answered: 11/25 question 12 simplify by writing as a single exponential expression. assume all variables are positive. $y^{\frac{1}{4}}y^{\frac{1}{4}}=$ question help: video written example

Explanation:

Step1: Apply exponent - product rule

When multiplying two exponential expressions with the same base \(a^m\cdot a^n=a^{m + n}\), here \(a = y\), \(m=\frac{1}{4}\), and \(n=\frac{1}{4}\). So \(y^{\frac{1}{4}}y^{\frac{1}{4}}=y^{\frac{1}{4}+\frac{1}{4}}\).

Step2: Add the exponents

\(\frac{1}{4}+\frac{1}{4}=\frac{1 + 1}{4}=\frac{2}{4}=\frac{1}{2}\). So \(y^{\frac{1}{4}+\frac{1}{4}}=y^{\frac{1}{2}}\).

Answer:

\(y^{\frac{1}{2}}\)